A tutorial on branch and cut algorithms for the maximum stable set problem

被引：24

作者：

Rebennack, Steffen ^{[1
]}

Reinelt, Gerhard ^{[2
]}

Pardalos, Panos M. ^{[3
]}

机构：

[1] Colorado Sch Mines, Div Econ & Business, Golden, CO 80401 USA

[2] Heidelberg Univ, Discrete Optimizat Res Grp, Heidelberg, Germany

[3] Univ Florida, Dept Ind & Syst Engn, Gainesville, FL 32611 USA

来源：

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH | 2012年 / 19卷 / 1-2期

关键词：

branch and cut; clique; cutting plane; separation; stable set; stable set polytope; TRAVELING SALESMAN PROBLEM; CLIQUE PROBLEM; WHEEL INEQUALITIES; OPTIMIZATION; RELAXATIONS; SEPARATION; POLYTOPES; GRAPHS;

D O I：

10.1111/j.1475-3995.2011.00805.x

中图分类号：

C93 [管理学];

学科分类号：

12 ; 1201 ; 1202 ; 120202 ;

摘要：

This tutorial provides an overview of various characteristics of effective branch and cut type algorithms for the maximum stable set problem. We discuss several facet-defining inequalities for the stable set polytope along with their separation routines. In particular, we review implementation tweaks for the separation routines and reference empirical studies, illustrating the performance of these cutting planes for benchmark graphs. In addition to the polyhedral study, we present basic preprocessing, discuss heuristic methods particularly suited within a branch and cut framework, and examine a branching rule.

引用

页码：161 / 199

页数：39

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